Coherent states for continuous spectrum operators with non-normalizable fiducial states

The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then we successfully apply the formalism to particular cases involving systems with a continuous spectrum: coherent states for the free particle and for the inverted oscillator (p2 − x2) are explicitly provided. Similar ideas can be used for other systems having non-normalizable fiducial states.